Haskell is a language which allows you to write type signatures for
functions, and even encourages you to do it.
Sometimes you even have to do it. Any language feature that stops
me from writing a type signature is in my opinion broken.
TFs as implemented in currently implemented ghc stops me from
writing type signatures. They are thus, in my opinion, broken.

The problem of ambiguity is not at all restricted to TFs. In fact,
you need neither TFs nor FDs to get the exact same behaviour. You
don't even need MPTCs:

/Users/chak/Code/haskell/Ambiguity.hs:10:7:
Could not deduce (C (a, b)) from the context (C (a1, b))
arising from a use of `bar'
at /Users/chak/Code/haskell/Ambiguity.hs:10:7-9
Possible fix:
add (C (a, b)) to the context of the type signature for `bar''
or add an instance declaration for (C (a, b))
In the expression: bar
In the definition of `bar'': bar' = bar

So, we have this problem as soon as we have flexible contexts and/or
MPTCs, independent of TFs and FDs.